Solve for $x$ and $y$ using elimination. ${-x+3y = 6}$ ${x-2y = -2}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x+3y = 6}\thinspace$ to find $x$ ${-x + 3}{(4)}{= 6}$ $-x+12 = 6$ $-x+12{-12} = 6{-12}$ $-x = -6$ $\dfrac{-x}{{-1}} = \dfrac{-6}{{-1}}$ ${x = 6}$ You can also plug ${y = 4}$ into $\thinspace {x-2y = -2}\thinspace$ and get the same answer for $x$ : ${x - 2}{(4)}{= -2}$ ${x = 6}$